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normalForm -- computes the normal form within the rational Weyl algebra

Description

This method computes the normal form of an element $P$ in the Weyl algebra $D_n$ with respect to another element in the Weyl algebra, or a whole list of such elements. The reduction step is carried out over the rational Weyl algebra $R_n$.

i1 : D = makeWA(QQ[x,y], {1,1});
i2 : P = dx^2 ; Q = x*dx+1;
i4 : normalForm(P, Q)

      2
o4 = --
      2
     x

o4 : frac(QQ[x..y])[dx, dy]

References

See [SST, Theorem 1.1.7].

Caveat

Due to technical limitations, the output lives in the graded associative algebra of the rational Weyl algebra, which is a commutative ring over the base fraction field of $D_n$ where the partial differentials are adjoined as commuting variables.

Ways to use normalForm:

  • normalForm(RingElement,List)
  • normalForm(RingElement,RingElement)

For the programmer

The object normalForm is a method function.


The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/ConnectionMatrices/docs.m2:96:0.